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Two-time-scale stochastic functional differential equations with wideband noises and jumps

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  • Liu, Yuanyuan
  • Wen, Zhexin

Abstract

This work examines a class of path-dependent stochastic systems which are hybrid with wideband noise, Poisson jumps and a singularly perturbed Markov chain. The addition of multi-scale Markov chain allows for modeling of discrete events with both fast and slow fluctuation. While this more realistic approach presents analytical challenges due to the non-Markovian formulation resulting from the wideband noise and the singularly perturbed Markov chain. By virtue of the weak convergence method and Itô functional formula, we prove that as ɛ→0, we obtain a Markovian switching jump diffusion. Finally, we offer several examples to illustrate our findings.

Suggested Citation

  • Liu, Yuanyuan & Wen, Zhexin, 2024. "Two-time-scale stochastic functional differential equations with wideband noises and jumps," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003084
    DOI: 10.1016/j.chaos.2024.114756
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    References listed on IDEAS

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